Abstract: Based on the density functional theory, the Perdew–Burke–Ernzerhof exchange-correlation potential was used to optimize the geometry of double perovskite Sr₂ReNbO₆ (Re=La, Gd, Lu) crystals, and the stable structures with lowest energy were obtained. Using the optimized structure as a model, the band structure and density of states (DOS), complex dielectric function ε(ω), refractive index n(ω), reflectivity R(ω) and distinction coefficient k(ω), and other optical properties of Sr₂ReNbO₆ (Re=La, Gd, Lu) crystals were calculated, and the influence of incident photon energy on the optical properties of the material was analyzed. The elastic constants C_ij of Sr₂ReNbO₆ (Re=La, Gd, Lu) crystals were also calculated, according to the C_ij, the mechanical properties include Young’s modulus (Y), bulk modulus (B), shear modulus (G) and Poisson’s ratio (χ) were further obtained, and the influence of crystal structure on the mechanical properties of the material was investigated. The results show that the lattice constants obtained from optimizing double perovskite crystal structure are in agreement with the available experimental values. The band structure of Sr₂ReNbO₆ (Re=La, Gd, Lu) materials exhibits the semiconductor characteristics, and the cubic Sr₂LaNbO₆ exhibits a direct band structure with bandgap of 3.12 eV, whereas the monoclinic Sr₂GdNbO₆ and Sr₂LuNbO₆ exhibit indirect band structure with bandgap of 3.25 eV and 3.29 eV, respectively. The maximum reflectivity R(ω) of Sr₂ReNbO₆(Re=La, Gd, Lu) are 32.8%, 29.3%, 33.0%, respectively, with a significant absorption coefficient in the ultraviolet region. The Poisson’s ratio (χ) of Sr₂ReNbO₆(Re=La, Gd, Lu) crystals are 0.27, 0.28, 0.27, respectively, all close to 0.25. The atoms in this series materials are probe to bond ionically, exhibiting a certain degree of flexibility.